Splicers are machines that provide a supply of web material to a web consuming process without interruption to reload the web material. In general, a roll of web material is consumed, and as it approaches depletion, is spliced to a new, replenishing roll without interrupting the supply of web material to the web consuming process. The instant invention is an improvement on the splicer invention covered in U.S. Pat. No. 8,002,924 B2 the disclosure of which is hereby incorporated by reference in this application. The present invention uses a similar roll unwind and accumulator arrangement as in the earlier splicer disclosed in U.S. Pat. No. 8,002,924. However, the portion of the apparatus and method used to splice a replenishing web to a depleting web is different from, and represents an improvement over, the corresponding arrangement in U.S. Pat. No. 8,002,924.